TY - JOUR
T1 - Parallel Computing Method of Pure Alternative Segment Explicit-Implicit Difference Scheme for Nonlinear Leland Equation
AU - Yan , Ruifang
AU - Yang , Xiaozhong
AU - Sun , Shuzhen
JO - Annals of Applied Mathematics
VL - 3
SP - 302
EP - 318
PY - 2022
DA - 2022/06
SN - 34
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20579.html
KW - nonlinear Leland equation, pure alternative segment explicit-implicit scheme (PASE-I), stability, truncation error analysis, parallel computing, numerical experiments.
AB - <p style="text-align: justify;">The research on the numerical solution of the nonlinear Leland equation
has important theoretical significance and practical value. To solve nonlinear
Leland equation, this paper offers a class of difference schemes with parallel nature which are pure alternative segment explicit-implicit (PASE-I) and
implicit-explicit (PASI-E) schemes. It also gives the existence and uniqueness,
the stability and the error estimate of numerical solutions for the parallel difference schemes. Theoretical analysis demonstrates that PASE-I and PASI-E
schemes have obvious parallelism, unconditionally stability and second-order
convergence in both space and time. The numerical experiments verify that
the calculation accuracy of PASE-I and PASI-E schemes are better than that of
the existing alternating segment Crank-Nicolson scheme, alternating segment
explicit-implicit and implicit-explicit schemes. The speedup of PASE-I scheme
is 9.89, compared to classical Crank-Nicolson scheme. Thus the schemes given
by this paper are highly efficient and practical for solving the nonlinear Leland
equation.</p>